Anharmonic vibrations of a nano-sized oscillator with fractional damping

We investigate the nonlinear vibrations of nano-sized cantilever. The elastic force is considered anharmonic, deriving from a Morse potential and the nonlinearity is attributed to the Casimir force. We consider two cases, the first of viscous damping and the second of fractional damping. lution is also established by using the Adomian decomposition method.